Question

How do you find the complex conjugate of `[4 - sqrt(-3)]/ 2`?

Answer 1

The complex conjugate of `(4-sqrt(-3))/2`
is
`2+sqrt(3)/2i`

Explanation:

First note
`color(white)("XXX")(4-sqrt(-3))/2 = 2-sqrt(3)/2i`

The complex conjugate of a complex number is
a number with
`color(white)("XXX")color(red)("the real component equal to the real component of the original number")`
and
`color(white)("XXX")color(blue)("the complex component equal in magnitude but opposite in sign.")`

So the complex conjugate of `color(red)(2)color(blue)(-sqrt(3)/2)i`
is `color(red)(2)color(blue)(+sqrt(3)/2)i`